In this article, we develop systematically second random phase approximations (RPA) and Tamm-Dancoff approximations (TDA) of particle-hole and particle-particle channels for calculating molecular excitation energies. The second particle-hole RPA/TDA can capture double excitations missed by the particle-hole RPA/TDA and time-dependent density-functional theory (TDDFT), while the second particle-particle RPA/TDA recovers non-highest-occupied-molecular-orbital excitations missed by the particle-particle RPA/TDA. With proper orbital restrictions, these restricted second RPAs and TDAs have a formal scaling of only O(N{sup 4}). The restricted versions of second RPAs and TDAs are tested with various small molecules to show some positive results. Data suggest that the restricted second particle-holemore » TDA (r2ph-TDA) has the best overall performance with a correlation coefficient similar to TDDFT, but with a larger negative bias. The negative bias of the r2ph-TDA may be induced by the unaccounted ground state correlation energy to be investigated further. Overall, the r2ph-TDA is recommended to study systems with both single and some low-lying double excitations with a moderate accuracy. Some expressions on excited state property evaluations, such as 〈S{sup ^2}〉 are also developed and tested.« less

The authors report calculations of the excitonic spectra for trans-polyacetylene obtained in the Hartree-Fock, Tamm-Danoff, and random-phase approximations. In the first case, in terms of two-particle propagator theory, the interaction between the excited electron and the hole is neglected. In the latter two cases, this interaction is considered in the first order. In this framework, the interaction between excitations of different bands and k-vectors has been included. They discuss the bandwidths and density of states for [pi]-[pi]*, [sigma]-[pi]*, [pi]-[sigma]*, and [sigma]-[sigma]*. 15 refs., 2 figs., 2 tabs.